Question

The table below represents the number of math problems Jana completed as a function of the number of minutes since she began doing her homework. Does this situation represent a linear or non-linear function, and why?

Jana’s Math Homework Progress
Minutes
Math Problems Completed
1
3
2
7
3
12
4
16
5
19
It represents a linear function because there is a constant rate of change.
It represents a linear function because there is not a constant rate of change.
It represents a non-linear function because there is a constant rate of change.
It represents a non-linear function because there is not a constant rate of change.

Answer 1

To determine whether the situation represents a linear or non-linear function, we can analyze the changes in the number of math problems completed as the minutes increase.

Let's look at the data more closely:

- From 1 minute to 2 minutes: \(7 - 3 = 4\) problems
- From 2 minutes to 3 minutes: \(12 - 7 = 5\) problems
- From 3 minutes to 4 minutes: \(16 - 12 = 4\) problems
- From 4 minutes to 5 minutes: \(19 - 16 = 3\) problems

Now, we see how the number of problems completed changes over time:
- The change in problems over the first interval (1 to 2 minutes) is 4.
- The change over the second interval (2 to 3 minutes) is 5.
- The change over the third interval (3 to 4 minutes) is 4.
- The change over the fourth interval (4 to 5 minutes) is 3.

Since the differences in the number of problems completed are **not constant**, it indicates that Jana's completion of math problems does not follow a linear relationship.

Based on this analysis, the correct answer is:

**It represents a non-linear function because there is not a constant rate of change.**